{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T00:17:52Z","timestamp":1649117872529},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2009,10]]},"abstract":"<jats:p> A new generalized Voronoi diagram, called a boat-sail Voronoi diagram, is defined on the basis of the time necessary for a boat to reach on water surface with flow. A new concept called a boat-sail distance is introduced on the surface of water with flow, and it is used to define a generalized Voronoi diagram, in such a way that the water surface is partitioned into regions belonging to the nearest harbors with respect to this distance. The problem of computing this Voronoi diagram is reduced to a boundary value problem of a partial differential equation, and a numerical method for solving this problem is constructed. The method is a modification of a so-called fast marching method originally proposed for the eikonal equation. Computational experiments show the efficiency and the stableness of the proposal method. We also apply our equation to the shortest path problem and the simulation of the forest fire. <\/jats:p>","DOI":"10.1142\/s0218195909003052","type":"journal-article","created":{"date-parts":[[2009,10,27]],"date-time":"2009-10-27T09:54:44Z","timestamp":1256637284000},"page":"425-440","source":"Crossref","is-referenced-by-count":2,"title":["BOAT-SAIL VORONOI DIAGRAM AND ITS APPLICATION"],"prefix":"10.1142","volume":"19","author":[{"given":"TETSUSHI","family":"NISHIDA","sequence":"first","affiliation":[{"name":"School of Business, University of Redlands, 1200 E. Colton Avenue, Redlands, California 92373, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"KOKICHI","family":"SUGIHARA","sequence":"additional","affiliation":[{"name":"Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashimita, Tamaku, Kawasaki 214-8571, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195999000169"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02293047"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01553882"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1007\/BF00164401","volume":"20","author":"Ash P. F.","journal-title":"Geometriae Dedicata"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0216006"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1145\/116873.116880"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0031-3203(84)90064-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-8176-4755-1"},{"key":"rf10","volume-title":"Methods of Mathematical Physics Volume II","author":"Courant R.","year":"1989"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386390"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1142\/9789814355858_0006"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1137\/0214006"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-739X(02)00033-X"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1145\/322217.322219"},{"key":"rf17","first-page":"145","volume":"33","author":"Miles R. E.","journal-title":"The Indian J. Statist."},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1002\/9780470317013"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.2307\/1427577"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598347059"},{"key":"rf24","volume-title":"Level Set Methods and Fast Marching Methods","author":"Sethian J. A.","year":"1999"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195992000032"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195909003052","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:24:23Z","timestamp":1565137463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195909003052"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,10]]},"references-count":20,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,10]]}},"alternative-id":["10.1142\/S0218195909003052"],"URL":"https:\/\/doi.org\/10.1142\/s0218195909003052","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,10]]}}}